The Golden Rule goes back to Biblical times. Jesus instructed his followers to "do unto others what you would have them do unto you." This rule is important in many religions other than Christianity, and in general is an important principle for children to learn. It is sometimes difficult to teach children about the Golden Rule, but it is well worth doing.
Children learn by example, so the best way to teach them about the Golden Rule is to practice it yourself and then verbalize what you are doing. For example, suppose you are invited to have supper with another couple that you don't particularly like. You might decide to go because it would make your husband happy to spend time with his friends. You can then explain to your children that even though you aren't really friends with these people and would rather stay home, it is important to Daddy, and you would want him to go to something that is important to you even though he doesn't really like the people. If you provide enough examples along with verbal explanations, your children will begin to internalize the rule.
You should also read stories to your children that demonstrate the Golden Rule, along with some stories that do not. After reading each story, you should discuss the characters' behaviors with your child. Ask your child for input as to whether the character's behavior was appropriate. In the course of discussion, make sure to refer to the principle of doing unto others as you would have them do unto you. In addition to using fictional stories, you can also talk to your children about current events, especially stories that involve children. Discuss what your child would have done in the place of a child featured in the news.
When your children are fighting with each other or otherwise misbehaving, this is a perfect time to reinforce the lesson. For example, if your child is upset because a sibling won't share a toy, you can encourage them to work it out and remind them of the Golden Rule. You can even ask them what they think this rule tells them they need to do. You can also use the Golden Rule to discourage your children from picking on classmates who are perceived to be different. If your child acts out and has to be put into time-out, once he or she is calm you may be able to discuss if he or she would want to be around another child who engaged in the negative behavior.
With a little bit of thought, almost any situation can be turned into a lesson about the Golden Rule. The more you expose your children to it, the more they will internalize and follow it.